Question

Find the semi perimeter of a triangle having side 10 cm, 24 cm, 26cm.​

Answer 1

Given :

•Find the semi perimeter of a triangle having sides 10 cm, 24cm,26cm

$\underline{\bf{To \: Find}}$

•The semi perimeter of a triangle=?

$\underline{\bf{Formula}}$

•$\boxed{\sf{Semi \: perimeter \: of \: triangle =\dfrac{a+b+c}{2}}}$

$\underline{\bf{Theory \: and \: Definition :}}$

•Triangle is a closed two-dimensional shape. It is a three-sided polygon. All sides are made of straight lines. The point where two straight lines join is the vertex. Hence, the triangle has three vertices. Each vertex forms an angle.

what is the perimeter of a triangle ?

•The sum of the lengths of the sides is the perimeter of any polygon.

In the case of a triangle,Perimeter = Sum of the three sides

Properties :

•A triangle has three sides and three angles.

•The sum of the angles of a triangle is always 180 degrees.

•The exterior angles of a triangle always add up to 360 degrees.

•The sum of consecutive interior and exterior angle is supplementary.

•The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

•The shortest side is always opposite the smallest interior angle. Similarly, the longest side is always opposite the largest interior angle.

$\boxed{\underline{\bf{Solution:}}}$

Let us consider that there are three sides of triangle are represented by a, b, c

Here,

•a=10cm

•b=24cm

•c=26cm

By using Formula :

$\\ \implies \sf \: semi \: perimeter \:of \: a \: triangle = \frac{a + b + c}{2}$

$\\ \implies \sf semi \: perimeter \: of \: a \: triangle = \frac{10 + 24 + 26}{2}$

$\\ \implies \sf \: semi \: perimeter \: of \:a \: triangle = \frac{34 + 26}{2}$

$\\ \implies \sf \: semi \: perimeter \: of \: a \: triangle = \frac{60}{2}$

$\\ \implies \boxed{ \sf{semi \: perimeter \: of \: a \: triangle = 30cm}}$